Americn Sector's shakes are awful, and should be skipped.
CC's are good, not great
Stanley's are quite good, and very close to where you are staying.
Camelia Grill's chocolate freeze is similar to a frozen hot chocolate at Serendipity, and is very refreshing.
Tru burger approach MVB, but I still think MVB are a smidge better.
Dunno about great, but Tru burger on Oak has milkshakes, as does the Milk Bar on Delachaise (or is it Aline?). And the mocha freeze at Camellia Grill isn't technically a milkshake, but it is quite tasty. Doesn't Stanley have shakes?
626 S Carrollton Ave, New Orleans, LA 70118